# How can I typeset long integral borders?

I currently would like to typeset an integral with long integral borders. But either I get too much space after the integral sign and before the function I integrate, or I get a wrong alignment of the border:

How can I typeset long integral borders?

## MWE

\documentclass[a5paper]{scrartcl}
\usepackage{amssymb, amsmath} % needed for math
\usepackage[utf8]{inputenc} % this is needed for umlauts
\usepackage[ngerman]{babel} % this is needed for umlauts
\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
\usepackage{mathtools}
\begin{document}
\section*{With mathclap}
\begin{align*}
\int_S f \mathrm{d} A &= \sum_{i=1}^n \int_{\mathclap{V_i}} f \mathrm{d} A \\
&- \sum_{i \neq j} \int_{\mathclap{V_i \cap V_j}} f \mathrm{d} A \\
&+ \sum_{i,j,k} \int_{\mathclap{V_i \cap V_j \cap V_k}} f \mathrm{d} A\\
&- \dots
\end{align*}

\section*{Without mathclap}
\begin{align*}
\int_S f \mathrm{d} A &= \sum_{i=1}^n \int_{V_i} f \mathrm{d} A \\
&- \sum_{i \neq j} \int_{V_i \cap V_j} f \mathrm{d} A \\
&+ \sum_{i,j,k} \int_{V_i \cap V_j \cap V_k} f \mathrm{d} A\\
&- \dots
\end{align*}
\end{document}

• Not recommending anything… but there exist \mathrlap and \mathllap just in case it works for you. – Manuel Feb 20 '14 at 14:39
• @Manuel that is exactly what I was looking for! Thank you! – Martin Thoma Feb 20 '14 at 14:41

\mathrlap{…} could do the job.

\documentclass[a5paper]{scrartcl}
\usepackage{amssymb, amsmath} % needed for math
\usepackage[utf8]{inputenc} % this is needed for umlauts
\usepackage[ngerman]{babel} % this is needed for umlauts
\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
\usepackage{mathtools}
\begin{document}
\section*{With mathrlap}
\begin{align*}
\int_S f \mathrm{d} A &= \sum_{i=1}^n \int_{\mathrlap{V_i}} f \mathrm{d} A \\
&- \sum_{i \neq j} \int_{\mathrlap{V_i \cap V_j}} f \mathrm{d} A \\
&+ \sum_{i,j,k} \int_{\mathrlap{V_i \cap V_j \cap V_k}} f \mathrm{d} A\\
&- \dots
\end{align*}

\section*{Without mathrlap}
\begin{align*}
\int_S f \mathrm{d} A &= \sum_{i=1}^n \int_{V_i} f \mathrm{d} A \\
&- \sum_{i \neq j} \int_{V_i \cap V_j} f \mathrm{d} A \\
&+ \sum_{i,j,k} \int_{V_i \cap V_j \cap V_k} f \mathrm{d} A\\
&- \dots
\end{align*}
\end{document}


Some hand tuning is necessary, with formulas like these.

\documentclass[a5paper]{scrartcl}
\usepackage{amsmath} % needed for math

\newcommand{\diff}{\mathop{}\!\mathrm{d}}
\newcommand{\back}[1]{\mspace{-#1mu}}

\begin{document}

\begin{align*}
\int_S f \diff A
&      = \sum_{i=1}^n    \; \int\limits_{V_i} f \diff A \\
&\quad - \sum_{i \neq j} \; \int\limits_{V_i \cap V_j}          \back{6} f \diff A \\
&\quad + \sum_{i,j,k}    \; \int\limits_{V_i \cap V_j \cap V_k} \back{12} f \diff A\\
\end{align*}
\end{document}


With \back you get some back spacing. The integration domain should be below the integral sign.

Don't use explicit \mathrm{d} for the differential (and don't use an upright “d”, but this is another matter), prefer a high level command. The one I propose automatically takes care of a thin space before the “d”.

\documentclass[a5paper]{scrartcl}
\usepackage{amssymb, amsmath} % needed for math
\usepackage[utf8]{inputenc} % this is needed for umlauts
\usepackage[ngerman]{babel} % this is needed for umlauts
\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
\usepackage{mathtools}
\usepackage{stackengine}
\stackMath
\begin{document}

\section*{With stacks}
\begin{align*}
\int_S f \mathrm{d} A &= \sum_{i=1}^n \stackunder{%
\displaystyle\int}{\scriptstyle V_i} f \mathrm{d} A \\
\displaystyle\int}{\rlap{$\scriptstyle V_i \cap V_j$}}} f \mathrm{d} A \\
\displaystyle\int}{\rlap{$\scriptstyle V_i \cap V_j\cap V_k$}}} f \mathrm{d} A \\